
where \(\mathrm {odds}(p) = \log (p (1-p)^{-1})\)  and \(p_{\mathrm {stable}}\)  and \(p_{\mathrm {prior}}\)  are probabilities for a stable surfel given a compatible measurement and the prior probability, respectively. The terms \(\exp (-x^2\sigma ^{-2})\)  are used to account for noisy measurements, where \(\alpha \)  is the angle between the surfel's normal \(\mathbf {n}_s\)  and the normal of the measurement to be integrated, and \(d\)  is the distance of the measurement in respect to the associated surfel.
The measurement normal is taken from \(\mathcal {N}_D\)  and the correspondences from the frame-to-model ICP, see [1]} for more details.
